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NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND W-POLYNOMIALS

JONATHAN DELENCLOS

Université d'Artois, Faculté Jean Perrin, Rue Jean Souvraz 62 307 Lens, France

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and

ANDRÉ LEROY

Université d'Artois, Faculté Jean Perrin, Rue Jean Souvraz 62 307 Lens, France

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https://doi.org/10.1142/S021949880700251XCited by:13 (Source: Crossref)

Abstract

Let K, S, D be a division ring, an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Viète formula and decompositions of differential operators. W-polynomials show up naturally, their connections with P-independency, Vandermonde and Wronskian matrices are briefly studied. The different linear factorizations of W-polynomials are analyzed. Connections between the existence of LLCM of monic linear polynomials with coefficients in a ring and the left duo property are established at the end of the paper.

Keywords:

AMSC: 16W35, 05E05

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